Interestingly, because of the payout structure of the non-jackpot prizes in Powerball, you actually have a lower chance of losing money playing two tickets than playing one. The smallest payout (for hitting the powerball and either 0 or 1 white balls) is $4 - the cost of two tickets - so, the chance of losing money playing two tickets is the chance that neither of them hits any prize (~93.82%), which is the square of the chance of either one individually hitting no prize (~96.86%).
The Secret of Monkey Island: Special Edition has been on the Mac App store since early 2011. But, the never did a Mac port of Monkey Island 2 SE. That one, though, is available for iOS.
Neutrinos are affected by gravity. Everything is. And, so far as general relativity is concerned, the paths that objects travel along under the influence of gravity (and nothing else) ARE the closest thing to straight line paths that actually exist.
It's not actually the neutrinos that produce the Cerenkov radiation in detectors. That only happens when a neutrino interacts in a way that either produces a high energy charged particle or gives a great deal of energy to a charged particle that is already present. In either case the need for an interaction with matter that's present in the detector means that such interactions will be very rare in vacuo; and, given how special the condition we need to actually see these events in detectors, it's unlikely that we would detect them in vacuo even if they happened. Further, since the Cerenkov radiation has to do with the speed of the charged particle, its presence or lack thereof wouldn't actually tell us about the mass of the neutrino.
The need to interact with something to "turn into other shit" is a requirement for transitions into other "real" particles. For instance, to actually get out an electron/positron pair from a high energy gamma ray, the gamma needs to interact. But, what we're actually talking about here are what are often term "virtual particles," which are better thought of as excitations in those particles' quantum fields that show up with the wrong mass to be real physical particles. These sorts of excitations happen spontaneously even without interactions, but very quickly transition back to the original state.
The necessity of mass is not an assumption and it has nothing to do with the passage of time. In short, oscillation can only occur if the neutrinos are produced in states that are a mixture of multiple physical states. Generically, the physical states are the ones that have well-defined values of mass. But, if all of the neutrinos have the same mass (whether it's 0 or not), then any mixture of the states is equally physical; so, the flavor states in which neutrinos are produced are, themselves, physical states, meaning that there's no mixing. So, it's not that they need to have mass, per se, it's that their masses need to differ from each other, meaning that at least two of the three states have to have non-zero mass.
Also, neutrinos can turn into other things in flight. For instance, an electron neutrino can briefly turn into an electron and a W^+ (well, in the same sense that a photon can "turn into" and electron and a positron, which isn't really quite a correct description, anyway). The thing is, because the mass of the W is so high, this sort of fluctuation is much rarer and lasts for a much shorter time. (This is where the statement about the weak force making these oscillations less relevant comes in.)
But, the problem with evidence for deviation from the speed of light is that, to not be an effect too small to measure, we would need to be looking at extremely low energy neutrinos. But, we don't actually have any ways to detect neutrinos with such small energies.
All that said, I actually have some issues with the idea presented. I haven't gone through the paper in detail; but, it seems like it's probably generating a violation of relativity by not actually working in a fully relativistic framework in the first place. It looks like the treatment of gravity may be too classical; but, that's just from a cursory look.
That's not why it's shut down. Government spending is split into two categories - mandatory and discretionary. Mandatory spending happens automatically; but, discretionary spending requires specific authorization from congress. If congress doesn't pass appropriation bills, discretionary spending stops. That's what happened here. It has nothing to do with revenue and everything to do with the Republicans in the House of Representatives refusing to pass appropriation bills that don't include language to end or delay the Affordable Care Act (which, it should be noted, mostly falls into the category of mandatory, not discretionary, spending).
To evaluate the merit of your argument it's necessary to consider the reasons for the decrease in fuel usage. Is it because (in the first example) people are actually traveling less total distance or is it because the conveyances being used waste less energy? If it's the later, improvements in efficiency will only have this effect for a finite time, as any useful process has a maximum possible efficiency determined (in essence) by the second law of thermodynamics. As technology gets closer to that limit, it will become increasingly difficult to achieve further advances in efficiency. At that point, we go back to increasing energy usage unless our behavior actually changes.
1) If we wait for nature to turn our energy consumption into an S-curve, the process will be extremely unpleasant for the people involved (constraints due to resource scarcity have a habit of fueling some rather nasty conflicts). It seems to me that we're better served to point out the problem so that we can try to find a way to limit our own energy use intentionally so that we can do it in a less painful way.
2) Even if population growth stops, energy growth doesn't necessarily. Per capita energy use has been increasing for pretty much all of human history. And, there's no reason to think that we aren't going to keep inventing new technologies that need ever more energy. (And, I should note here that most improvements in energy efficiency work by reducing the amount of energy that goes to waste heat, not by reducing the amount of energy required for the purpose for which we're expending energy. CFLs and LED light bulbs put out the same amount of energy in light as do incandescents; but, they give off less heat, for example.) If this continues, we'll still have a problem.
3) Expanding into the galaxy still has a non-exponential limit on our growth. In that case, at best we increase the available space and energy resources quadratically, since our outward expansion is limited by the speed of light.
4) Human ingenuity does not trump physics. If there are no new energy resources to tap, no amount of cleverness will allow growth in energy use to continue. And, please note, zero point energy is not a magical reservoir of unlimited energy waiting to be tapped.
5) I don't have to believe that today's conception of physics is 100% correct (and, in fact, I can tell you with 100% certainty that our current understanding of physics is, at best, incomplete) to be extremely confident that there aren't major unknown sources of available energy that can supersede the output of the sun. I can conclude this because the only phenomena that are not fully explained by known physics are things that couple only extremely weakly to the ordinary matter we are able to exert direct control over. So, any major untapped sources of energy either don't exist or are not accessible in any practical way.
6) Even ignoring the point that cold fusion is total nonsense (fusion in general is not; but, cold fusion has been shown, time and again, to be totally unsupported by the evidence), any energy source reliant on materials present on Earth will be, at best, a temporary solution. Eventually, solar will be the only source practically available.
7) Finally, TFA doesn't need to consider "a lot more obvious possibilities" when they can all be dismissed as having far less total energy available than the sun. Maybe other technologies can allow us to use energy faster than the sun outputs for a time; but, ultimately, that's just putting off the inevitable limitations for a finite (and, frankly, surprisingly short) time, unless we learn to stem our energy use.
Congratulations. You've found a way to extend the possible horizon of energy use growth from 300 years to 1250 years. But, it doesn't solve the problem. At 2.3% annual growth, we'll need to be using 100% or the sun's output in about 1250 years. Then what? Your self-replicating space habitats don't give us any new sources of energy. At best, they just increase the surface area we can use to capture solar radiation. It simply doesn't change that fact that exponential growth in energy use is not physically sustainable in the long term.
Model dependence isn't really relevant here. The point is that, even if the entire three hour delay were blamed on the neutrinos being superluminal rather than the light being delayed (which physics does say it has to be), the degree by which the SN1987a neutrinos would be faster than light is 4 orders of magnitude smaller than what the OPERA results claim.
Quarks have the same sort of mixing as neutrinos. The only real difference is that the low mass and small couplings of neutrinos make it much easier for us to think about neutrinos in terms of flavor states (i.e. electron, muon, and tau neutrinos) rather than mass states, which is what we're pretty much forced to use for quarks.
Anyway, neutrino mixing is totally consistent with relativity; and, in fact, almost required for massive neutrinos in quantum field theory. The only reason it was a surprising result in the first place is that there had been no previous evidence that neutrinos have mass.
Superluminal neutrinos, on the other hand, are really not consistent with existing theories; so, they are, quite rightly, taken with a great deal of skepticism, at least until independently confirmed, or until all possible sources of systematic errors that could mimic the effect are ruled out.
I think you mean "flavor." Chirality is just one basis that happens to be particularly useful in talking about spin. It has nothing to do with the 3 types of neutrinos.
Whomever wrote that was talking out of, err, where the photons don't shine. Just like they don't shine through 730 km of solid rock. The experiment compares the measured neutrino speed with the previously known speed of light. It's not performed as a race between photons and neutrinos.
I think the actual number is more like a little under 4 years. Either way, though, two of the three detectors that detected the SN1987A burst were operating during that time period.
A more important point, though, is the sheer improbability of those three experiments detecting 24 neutrinos in a span of 13 seconds. The detection at KamiokaNDE alone had a probability of occurring randomly of no greater than 0.00000057%.
How do they both know a priori that the particles they're measuring are entangled?
Put another way, the only information that exists in this problem is the fact that the particles are entangled and the state that one of them ends up in. For such a situation to allow superluminal communication, it would be necessary that one of these pieces of information be able to be chosen by Alice or Bob. But, the fact that they both know about the entanglement to begin with means that information is only transferred if an experimenter can pick which state her particle ends up in, which isn't possible in the sort of measurements which won't break the entanglement.
That would be a fair point, except that the issue here isn't how well you can measure a time interval at one location. The issue is how well you can synchronize two clocks which are situated 730 km apart. GPS is actually a pretty good way of doing this because both labs can receive signals sent from some subset of the GPS satellites at any given time, giving a common reference. The actual time measurements are performed with atomic clocks at each end.
Again, no. The relationship between an object's invariant mass and its "relativistic mass" (which, again, is really just another way of saying "energy") in a particular frame is really quite simple:
m = m_0/\sqrt{1-(v/c)^2}
It has nothing to do with the power necessary to accelerate to a given speed, and it rises at exactly the rate I indicated.
Now, if you want to talk total power consumption, you need to know the energy to mass ratio of any fuel you need to carry, just as you would for a totally classical rocket. But, frankly that's an unnecessary complication since we could just as easily talk about a system that needs to carry no fuel - a solar sail, for instance.
The fact that the invariant mass of a proton is not the sum of the invariant masses of its constituent quarks (or even, their combined invariant mass) isn't really relevant here. It's just as meaningful to talk about the invariant mass of the proton (which is also a scalar) as it is to talk about the invariant mass of an electron or the invariant mass of an astronaut. The physical origin of that mass (the Higgs mechanism, QCD binding energy, or, for that matter, any other kind of binding energy or internal kinetic energy) doesn't really affect anything about how it is most reasonable to look at the full system. (As a side note, I don't think you mean "quark-gluon plasma." That's a high energy phase of matter created the presence of unconfined quarks and gluons. What you're talking about here is simply QCD binding energy.)
Slashdot Mirror
"Pocket rockets"? Uh, I'm pretty sure that term's already taken...
Interestingly, because of the payout structure of the non-jackpot prizes in Powerball, you actually have a lower chance of losing money playing two tickets than playing one. The smallest payout (for hitting the powerball and either 0 or 1 white balls) is $4 - the cost of two tickets - so, the chance of losing money playing two tickets is the chance that neither of them hits any prize (~93.82%), which is the square of the chance of either one individually hitting no prize (~96.86%).
The Secret of Monkey Island: Special Edition has been on the Mac App store since early 2011. But, the never did a Mac port of Monkey Island 2 SE. That one, though, is available for iOS.
Neutrinos are affected by gravity. Everything is. And, so far as general relativity is concerned, the paths that objects travel along under the influence of gravity (and nothing else) ARE the closest thing to straight line paths that actually exist.
It's not actually the neutrinos that produce the Cerenkov radiation in detectors. That only happens when a neutrino interacts in a way that either produces a high energy charged particle or gives a great deal of energy to a charged particle that is already present. In either case the need for an interaction with matter that's present in the detector means that such interactions will be very rare in vacuo; and, given how special the condition we need to actually see these events in detectors, it's unlikely that we would detect them in vacuo even if they happened. Further, since the Cerenkov radiation has to do with the speed of the charged particle, its presence or lack thereof wouldn't actually tell us about the mass of the neutrino.
The need to interact with something to "turn into other shit" is a requirement for transitions into other "real" particles. For instance, to actually get out an electron/positron pair from a high energy gamma ray, the gamma needs to interact. But, what we're actually talking about here are what are often term "virtual particles," which are better thought of as excitations in those particles' quantum fields that show up with the wrong mass to be real physical particles. These sorts of excitations happen spontaneously even without interactions, but very quickly transition back to the original state.
The necessity of mass is not an assumption and it has nothing to do with the passage of time. In short, oscillation can only occur if the neutrinos are produced in states that are a mixture of multiple physical states. Generically, the physical states are the ones that have well-defined values of mass. But, if all of the neutrinos have the same mass (whether it's 0 or not), then any mixture of the states is equally physical; so, the flavor states in which neutrinos are produced are, themselves, physical states, meaning that there's no mixing. So, it's not that they need to have mass, per se, it's that their masses need to differ from each other, meaning that at least two of the three states have to have non-zero mass.
Also, neutrinos can turn into other things in flight. For instance, an electron neutrino can briefly turn into an electron and a W^+ (well, in the same sense that a photon can "turn into" and electron and a positron, which isn't really quite a correct description, anyway). The thing is, because the mass of the W is so high, this sort of fluctuation is much rarer and lasts for a much shorter time. (This is where the statement about the weak force making these oscillations less relevant comes in.)
But, the problem with evidence for deviation from the speed of light is that, to not be an effect too small to measure, we would need to be looking at extremely low energy neutrinos. But, we don't actually have any ways to detect neutrinos with such small energies.
All that said, I actually have some issues with the idea presented. I haven't gone through the paper in detail; but, it seems like it's probably generating a violation of relativity by not actually working in a fully relativistic framework in the first place. It looks like the treatment of gravity may be too classical; but, that's just from a cursory look.
Not to mention that the federal Medicaid payments are actually block grants to the states.
That's not why it's shut down. Government spending is split into two categories - mandatory and discretionary. Mandatory spending happens automatically; but, discretionary spending requires specific authorization from congress. If congress doesn't pass appropriation bills, discretionary spending stops. That's what happened here. It has nothing to do with revenue and everything to do with the Republicans in the House of Representatives refusing to pass appropriation bills that don't include language to end or delay the Affordable Care Act (which, it should be noted, mostly falls into the category of mandatory, not discretionary, spending).
Or it could mean that they actually care about the work they're doing.
To evaluate the merit of your argument it's necessary to consider the reasons for the decrease in fuel usage. Is it because (in the first example) people are actually traveling less total distance or is it because the conveyances being used waste less energy? If it's the later, improvements in efficiency will only have this effect for a finite time, as any useful process has a maximum possible efficiency determined (in essence) by the second law of thermodynamics. As technology gets closer to that limit, it will become increasingly difficult to achieve further advances in efficiency. At that point, we go back to increasing energy usage unless our behavior actually changes.
1) If we wait for nature to turn our energy consumption into an S-curve, the process will be extremely unpleasant for the people involved (constraints due to resource scarcity have a habit of fueling some rather nasty conflicts). It seems to me that we're better served to point out the problem so that we can try to find a way to limit our own energy use intentionally so that we can do it in a less painful way.
2) Even if population growth stops, energy growth doesn't necessarily. Per capita energy use has been increasing for pretty much all of human history. And, there's no reason to think that we aren't going to keep inventing new technologies that need ever more energy. (And, I should note here that most improvements in energy efficiency work by reducing the amount of energy that goes to waste heat, not by reducing the amount of energy required for the purpose for which we're expending energy. CFLs and LED light bulbs put out the same amount of energy in light as do incandescents; but, they give off less heat, for example.) If this continues, we'll still have a problem.
3) Expanding into the galaxy still has a non-exponential limit on our growth. In that case, at best we increase the available space and energy resources quadratically, since our outward expansion is limited by the speed of light.
4) Human ingenuity does not trump physics. If there are no new energy resources to tap, no amount of cleverness will allow growth in energy use to continue. And, please note, zero point energy is not a magical reservoir of unlimited energy waiting to be tapped.
5) I don't have to believe that today's conception of physics is 100% correct (and, in fact, I can tell you with 100% certainty that our current understanding of physics is, at best, incomplete) to be extremely confident that there aren't major unknown sources of available energy that can supersede the output of the sun. I can conclude this because the only phenomena that are not fully explained by known physics are things that couple only extremely weakly to the ordinary matter we are able to exert direct control over. So, any major untapped sources of energy either don't exist or are not accessible in any practical way.
6) Even ignoring the point that cold fusion is total nonsense (fusion in general is not; but, cold fusion has been shown, time and again, to be totally unsupported by the evidence), any energy source reliant on materials present on Earth will be, at best, a temporary solution. Eventually, solar will be the only source practically available.
7) Finally, TFA doesn't need to consider "a lot more obvious possibilities" when they can all be dismissed as having far less total energy available than the sun. Maybe other technologies can allow us to use energy faster than the sun outputs for a time; but, ultimately, that's just putting off the inevitable limitations for a finite (and, frankly, surprisingly short) time, unless we learn to stem our energy use.
Congratulations. You've found a way to extend the possible horizon of energy use growth from 300 years to 1250 years. But, it doesn't solve the problem. At 2.3% annual growth, we'll need to be using 100% or the sun's output in about 1250 years. Then what? Your self-replicating space habitats don't give us any new sources of energy. At best, they just increase the surface area we can use to capture solar radiation. It simply doesn't change that fact that exponential growth in energy use is not physically sustainable in the long term.
But, they weren't. In fact, the supernova neutrinos had energies only about 1% of those of the OPERA neutrinos.
Model dependence isn't really relevant here. The point is that, even if the entire three hour delay were blamed on the neutrinos being superluminal rather than the light being delayed (which physics does say it has to be), the degree by which the SN1987a neutrinos would be faster than light is 4 orders of magnitude smaller than what the OPERA results claim.
Quarks have the same sort of mixing as neutrinos. The only real difference is that the low mass and small couplings of neutrinos make it much easier for us to think about neutrinos in terms of flavor states (i.e. electron, muon, and tau neutrinos) rather than mass states, which is what we're pretty much forced to use for quarks. Anyway, neutrino mixing is totally consistent with relativity; and, in fact, almost required for massive neutrinos in quantum field theory. The only reason it was a surprising result in the first place is that there had been no previous evidence that neutrinos have mass. Superluminal neutrinos, on the other hand, are really not consistent with existing theories; so, they are, quite rightly, taken with a great deal of skepticism, at least until independently confirmed, or until all possible sources of systematic errors that could mimic the effect are ruled out.
I think you mean "flavor." Chirality is just one basis that happens to be particularly useful in talking about spin. It has nothing to do with the 3 types of neutrinos.
Whomever wrote that was talking out of, err, where the photons don't shine. Just like they don't shine through 730 km of solid rock. The experiment compares the measured neutrino speed with the previously known speed of light. It's not performed as a race between photons and neutrinos.
Two problems. First, how do you arrange for that difference? Second, what about the neutrinos on the leading edge?
That would involve a longer path length than the neutrinos traveled. So, no go there.
I think the actual number is more like a little under 4 years. Either way, though, two of the three detectors that detected the SN1987A burst were operating during that time period. A more important point, though, is the sheer improbability of those three experiments detecting 24 neutrinos in a span of 13 seconds. The detection at KamiokaNDE alone had a probability of occurring randomly of no greater than 0.00000057%.
How do they both know a priori that the particles they're measuring are entangled? Put another way, the only information that exists in this problem is the fact that the particles are entangled and the state that one of them ends up in. For such a situation to allow superluminal communication, it would be necessary that one of these pieces of information be able to be chosen by Alice or Bob. But, the fact that they both know about the entanglement to begin with means that information is only transferred if an experimenter can pick which state her particle ends up in, which isn't possible in the sort of measurements which won't break the entanglement.
That would be a fair point, except that the issue here isn't how well you can measure a time interval at one location. The issue is how well you can synchronize two clocks which are situated 730 km apart. GPS is actually a pretty good way of doing this because both labs can receive signals sent from some subset of the GPS satellites at any given time, giving a common reference. The actual time measurements are performed with atomic clocks at each end.
Again, no. The relationship between an object's invariant mass and its "relativistic mass" (which, again, is really just another way of saying "energy") in a particular frame is really quite simple:
m = m_0/\sqrt{1-(v/c)^2}
It has nothing to do with the power necessary to accelerate to a given speed, and it rises at exactly the rate I indicated.
Now, if you want to talk total power consumption, you need to know the energy to mass ratio of any fuel you need to carry, just as you would for a totally classical rocket. But, frankly that's an unnecessary complication since we could just as easily talk about a system that needs to carry no fuel - a solar sail, for instance.
The fact that the invariant mass of a proton is not the sum of the invariant masses of its constituent quarks (or even, their combined invariant mass) isn't really relevant here. It's just as meaningful to talk about the invariant mass of the proton (which is also a scalar) as it is to talk about the invariant mass of an electron or the invariant mass of an astronaut. The physical origin of that mass (the Higgs mechanism, QCD binding energy, or, for that matter, any other kind of binding energy or internal kinetic energy) doesn't really affect anything about how it is most reasonable to look at the full system. (As a side note, I don't think you mean "quark-gluon plasma." That's a high energy phase of matter created the presence of unconfined quarks and gluons. What you're talking about here is simply QCD binding energy.)